Because the scientific and business worlds operate in a decimal system while the overwhelming majority of digital computers operate in a binary system (binary logic being cheaper, more reliable, and simpler), many apparatuses and methods have been devised for converting binary fractions to Binary Coded Decimal (BCD) or decimal form. However, these prior art approaches have been complex and have required intricate circuitry in performing the conversion. One such apparatus is outlined in U.S. Pat. No. 3,257,547. The converter therein described includes elegant logic units which successively multiply a fractional binary input by the decimal number ten (1010 in binary form) and then take the four most significant bits resulting from each multiplication process as the next most significant BCD digit of the output. In accomplishing this conversion, the described prior art apparatus executes two cycles, i.e., a shift cycle and a fix-up cycle. In operation, a fractional binary number to be converted is shifted out, one bit each cycle, least significant bit first, into a series of BCD units each having four flip-flops arranged to represent the binary coded decimal digit. During the fix-up cycle, the most significant bit of the four bits which enter each BCD unit is examined and, if it is a binary 1, an appropriate logically-determined number is subtracted from the shifted out number with the result being placed in the four flip-flops in BCD form. By employing these two cycles alternately, a complete binary to BCD conversion is effected in a number of cycles equal to the number of initial binary bits in the binary number.
The described prior art converter requires logic units which operate on the binary fraction in accordance with a series of Boolean equations. For example, according to the Boolean equations, the conversion of 1/16 (.0001 in binary) would include a first step shifting the least significant bit, 1, into the most significant digit flip-flop of a first four-digit BCD unit which reads the resulting BCD number as 8 (1000 in binary). By Boolean methods, the converter "fixes up" the resulting BCD number by subtracting 3 (0011 in binary) from 8 (1000 in binary) to give 5 (0101 in binary) in the most significant BCD unit. At this point in the conversion the BCD units together hold a value .5000 . . . . The 5 is then shifted to the most significant digit flip-flop of a second, third, and successive units (as more significant bits of the binary fraction word are shifted in) until it ends up in the --5-- position. After a number of other logical operations, a final decimal equivalent value of .0625 . . . is extracted corresponding to the initial binary .0001 (1/16). The logic units to "fix-up the BCD number and the gating networks, which implement the Boolean equations, greatly complicate the operation of this prior art converter.